Hellenistic Science: Euclid, Aristarchus, & Archimedes HPS 340.
MEASURING THE SOLAR SYSTEM Eratosthenes, Aristarchus The century after Euclid.
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MEASURING THE SOLAR SYSTEM Eratosthenes, Aristarchus The century after Euclid
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Transcript of MEASURING THE SOLAR SYSTEM Eratosthenes, Aristarchus The century after Euclid.
MEASURING THE SOLAR SYSTEM
Eratosthenes, Aristarchus
The century after Euclid
SHADOWS
SIZE OF EARTH
ERATOSTHENES - 225 BC
ERATOSTHENESBELIEVED EARTH TO BE SPHERICAL
SUN’S RAYS NEARLY PARALLEL
THEREFORE SUN’S RAYS ARRIVE AT DIFFERENT ANGLES
AT DIFFERENT LOCATIONS
SIZE OF EARTH
• ON JUNE 21, AT NOON, THE SUN IS DIRECTLY OVERHEAD AT SYENE, EGYPT.
SIZE OF EARTH• ERATOSTHENES MEASURED THE
ANGLE OF THE SUN AT ALEXANDRIA, 5000 STADES NORTH, ON THE SAME DATE, FINDING IT WAS 1/50 OF A FULL CIRCLE FROM OVERHEAD.
THE PROBLEM HAS BEEN REDUCED TO GEOMETRY
SYENE
ALEXANDRIA
ALEXANDRIA
SYENE
ALEXANDRIA MUST BE 1/50 OF THE EARTH’S CIRCUMFERENCE NORTH
OF SYENE, SO THE CIRCUMFERENCE MUST BE 250,000
STADES, OR ABOUT 28,000 MILES
SHADOWS: DISTANCE TO THE MOON
SHADOW OF THE EARTH IN SPACE
D
108 D
ARISTAUCHUS 250 BCE
UMBRA AND PENUMBRA
DURING A LUNAR ECLIPSE, THE MOON PASSES THROUGH THE SHADOW OF THE EARTH
OBSERVATIONS
THE SHADOW IS 2 1/2 TIMES THE MOON’S DIAMETER
ANGULAR SIZE OF MOON = ANGULAR SIZE OF SUN
THE PROBLEM HAS BEEN REDUCED TO GEOMETRY
d
2.5d
BC = 2.5 AB
AC = BC + AB = 2.5AB + AB =3.5 AB
AB = AC/3.5 = 108D/3.5 = 31D
B
A
CD
E
MoonSun
Earth
900
ARISTARCHUS: DISTANCE TO THE SUN
Date Astronomer Moon Distance Sun Distance -260 Aristarchus 9.5 180
-130 Hipparchus 33.7 1245
-70 Posidonius 26.2 6545
+150 Ptolemy 29.5 605
Modern Values 30.3 11,745
SUMMARY: GREEK DISTANCES IN EARTH
DIAMETERS
ARISTARCHUS’ HELIOCENTRIC MODEL
SUN IS AT CENTER
EARTH ROTATES DAILY PRODUCINGTHE APPARENT DAILY MOTIONS
OF THE CELESTIAL OBJECTS
EARTH ORBITS SUN ONCE PER YEARPRODUCING THE PROGRESSION
THROUGH THE ZODIAC
1. Lack of stellar parallax.
2. Required overthrowing a long-established conventional wisdom.
3. The earth feels like it is stationary. If we evaluate the earth’s orbital speed required by the heliocentric model, even using Aristarchus’ small value for the distance to the sun, we find v = 2R/365 = 25,000 miles/day. This was an unheard of speed, and we don’t notice it. Galileo was the first person to correctly address this question and to explain it.
4. Religious and cultural reasons. Accepting this radical change in world view would require changing the jobs of many of the gods (e.g. Zeus, who carried the Sun across the sky). It also displaces humans from the center of the universe.
SUMMARY
